Effective elasticity tensors of fiber-reinforced composite materials with 2D or 3D fiber distribution coefficients
Abstract A fiber-reinforced composite material %$\mathcal {N}%$ consists of a matrix and numerous fibers. Besides their intrinsic properties and the volume fractions of matrix and fibers, the effective elasticity tensors of %$\mathcal {N}%$ are also related to the two-dimensional (2D) or the three-d...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Zhao, Tengfei [verfasserIn] Zhang, Lei [verfasserIn] Huang, Mojia [verfasserIn] |
|---|
| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019 |
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| Übergeordnetes Werk: |
Enthalten in: Acta mechanica - Wien : Springer, 1965, 230(2019), 12 vom: 12. Aug., Seite 4175-4195 |
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| Übergeordnetes Werk: |
volume:230 ; year:2019 ; number:12 ; day:12 ; month:08 ; pages:4175-4195 |
| Links: |
|---|
| DOI / URN: |
10.1007/s00707-019-02485-w |
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| Katalog-ID: |
SPR007513062 |
|---|
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| 100 | 1 | |a Zhao, Tengfei |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Effective elasticity tensors of fiber-reinforced composite materials with 2D or 3D fiber distribution coefficients |
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| 520 | |a Abstract A fiber-reinforced composite material %$\mathcal {N}%$ consists of a matrix and numerous fibers. Besides their intrinsic properties and the volume fractions of matrix and fibers, the effective elasticity tensors of %$\mathcal {N}%$ are also related to the two-dimensional (2D) or the three-dimensional (3D) fiber direction distributions. Herein the Fourier series and the Wigner D-functions are introduced as the 2D and the 3D fiber direction distribution functions (FDF), respectively. The expanded coefficients of the FDF are called the fiber distribution coefficients (FDC). When %$\mathcal {N}%$ consists of an anisotropic elasticity matrix and numerous transversely isotropic fibers, we derive the effective elasticity tensor %$\widehat{\mathbf {C}}%$ of %$\mathcal {N}%$ by the self-consistent method with the 2D FDC or the 3D FDC. The FDC can be easily obtained via the fiber direction arrangements of %$\mathcal {N}%$ for the fiber arbitrary or orthorhombic distributions of %$\mathcal {N}%$. The procedure of deriving %$\widehat{\mathbf {C}}%$ is simple because the Kelvin notation is used to compute tensor rotations. When both the matrix and the fibers are isotropic, for the 2D fiber distributions at least three direction arrangements of fibers are needed to build the fiber-reinforced transversely isotropic composite materials, and for the 3D fiber distributions at least six direction arrangements are needed to build the fiber-reinforced isotropic composite materials. The results of the FEM simulations are consistent with those of our expressions %$\widehat{\mathbf {C}}%$. | ||
| 700 | 1 | |a Zhang, Lei |e verfasserin |4 aut | |
| 700 | 1 | |a Huang, Mojia |e verfasserin |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Acta mechanica |d Wien : Springer, 1965 |g 230(2019), 12 vom: 12. Aug., Seite 4175-4195 |w (DE-627)270126139 |w (DE-600)1476343-6 |x 1619-6937 |7 nnns |
| 773 | 1 | 8 | |g volume:230 |g year:2019 |g number:12 |g day:12 |g month:08 |g pages:4175-4195 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s00707-019-02485-w |z lizenzpflichtig |3 Volltext |
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10.1007/s00707-019-02485-w doi (DE-627)SPR007513062 (SPR)s00707-019-02485-w-e DE-627 ger DE-627 rakwb eng 530 ASE 50.31 bkl 50.33 bkl 33.11 bkl Zhao, Tengfei verfasserin aut Effective elasticity tensors of fiber-reinforced composite materials with 2D or 3D fiber distribution coefficients 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract A fiber-reinforced composite material %$\mathcal {N}%$ consists of a matrix and numerous fibers. Besides their intrinsic properties and the volume fractions of matrix and fibers, the effective elasticity tensors of %$\mathcal {N}%$ are also related to the two-dimensional (2D) or the three-dimensional (3D) fiber direction distributions. Herein the Fourier series and the Wigner D-functions are introduced as the 2D and the 3D fiber direction distribution functions (FDF), respectively. The expanded coefficients of the FDF are called the fiber distribution coefficients (FDC). When %$\mathcal {N}%$ consists of an anisotropic elasticity matrix and numerous transversely isotropic fibers, we derive the effective elasticity tensor %$\widehat{\mathbf {C}}%$ of %$\mathcal {N}%$ by the self-consistent method with the 2D FDC or the 3D FDC. The FDC can be easily obtained via the fiber direction arrangements of %$\mathcal {N}%$ for the fiber arbitrary or orthorhombic distributions of %$\mathcal {N}%$. The procedure of deriving %$\widehat{\mathbf {C}}%$ is simple because the Kelvin notation is used to compute tensor rotations. When both the matrix and the fibers are isotropic, for the 2D fiber distributions at least three direction arrangements of fibers are needed to build the fiber-reinforced transversely isotropic composite materials, and for the 3D fiber distributions at least six direction arrangements are needed to build the fiber-reinforced isotropic composite materials. The results of the FEM simulations are consistent with those of our expressions %$\widehat{\mathbf {C}}%$. Zhang, Lei verfasserin aut Huang, Mojia verfasserin aut Enthalten in Acta mechanica Wien : Springer, 1965 230(2019), 12 vom: 12. Aug., Seite 4175-4195 (DE-627)270126139 (DE-600)1476343-6 1619-6937 nnns volume:230 year:2019 number:12 day:12 month:08 pages:4175-4195 https://dx.doi.org/10.1007/s00707-019-02485-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 50.31 ASE 50.33 ASE 33.11 ASE AR 230 2019 12 12 08 4175-4195 |
| spelling |
10.1007/s00707-019-02485-w doi (DE-627)SPR007513062 (SPR)s00707-019-02485-w-e DE-627 ger DE-627 rakwb eng 530 ASE 50.31 bkl 50.33 bkl 33.11 bkl Zhao, Tengfei verfasserin aut Effective elasticity tensors of fiber-reinforced composite materials with 2D or 3D fiber distribution coefficients 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract A fiber-reinforced composite material %$\mathcal {N}%$ consists of a matrix and numerous fibers. Besides their intrinsic properties and the volume fractions of matrix and fibers, the effective elasticity tensors of %$\mathcal {N}%$ are also related to the two-dimensional (2D) or the three-dimensional (3D) fiber direction distributions. Herein the Fourier series and the Wigner D-functions are introduced as the 2D and the 3D fiber direction distribution functions (FDF), respectively. The expanded coefficients of the FDF are called the fiber distribution coefficients (FDC). When %$\mathcal {N}%$ consists of an anisotropic elasticity matrix and numerous transversely isotropic fibers, we derive the effective elasticity tensor %$\widehat{\mathbf {C}}%$ of %$\mathcal {N}%$ by the self-consistent method with the 2D FDC or the 3D FDC. The FDC can be easily obtained via the fiber direction arrangements of %$\mathcal {N}%$ for the fiber arbitrary or orthorhombic distributions of %$\mathcal {N}%$. The procedure of deriving %$\widehat{\mathbf {C}}%$ is simple because the Kelvin notation is used to compute tensor rotations. When both the matrix and the fibers are isotropic, for the 2D fiber distributions at least three direction arrangements of fibers are needed to build the fiber-reinforced transversely isotropic composite materials, and for the 3D fiber distributions at least six direction arrangements are needed to build the fiber-reinforced isotropic composite materials. The results of the FEM simulations are consistent with those of our expressions %$\widehat{\mathbf {C}}%$. Zhang, Lei verfasserin aut Huang, Mojia verfasserin aut Enthalten in Acta mechanica Wien : Springer, 1965 230(2019), 12 vom: 12. Aug., Seite 4175-4195 (DE-627)270126139 (DE-600)1476343-6 1619-6937 nnns volume:230 year:2019 number:12 day:12 month:08 pages:4175-4195 https://dx.doi.org/10.1007/s00707-019-02485-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 50.31 ASE 50.33 ASE 33.11 ASE AR 230 2019 12 12 08 4175-4195 |
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10.1007/s00707-019-02485-w doi (DE-627)SPR007513062 (SPR)s00707-019-02485-w-e DE-627 ger DE-627 rakwb eng 530 ASE 50.31 bkl 50.33 bkl 33.11 bkl Zhao, Tengfei verfasserin aut Effective elasticity tensors of fiber-reinforced composite materials with 2D or 3D fiber distribution coefficients 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract A fiber-reinforced composite material %$\mathcal {N}%$ consists of a matrix and numerous fibers. Besides their intrinsic properties and the volume fractions of matrix and fibers, the effective elasticity tensors of %$\mathcal {N}%$ are also related to the two-dimensional (2D) or the three-dimensional (3D) fiber direction distributions. Herein the Fourier series and the Wigner D-functions are introduced as the 2D and the 3D fiber direction distribution functions (FDF), respectively. The expanded coefficients of the FDF are called the fiber distribution coefficients (FDC). When %$\mathcal {N}%$ consists of an anisotropic elasticity matrix and numerous transversely isotropic fibers, we derive the effective elasticity tensor %$\widehat{\mathbf {C}}%$ of %$\mathcal {N}%$ by the self-consistent method with the 2D FDC or the 3D FDC. The FDC can be easily obtained via the fiber direction arrangements of %$\mathcal {N}%$ for the fiber arbitrary or orthorhombic distributions of %$\mathcal {N}%$. The procedure of deriving %$\widehat{\mathbf {C}}%$ is simple because the Kelvin notation is used to compute tensor rotations. When both the matrix and the fibers are isotropic, for the 2D fiber distributions at least three direction arrangements of fibers are needed to build the fiber-reinforced transversely isotropic composite materials, and for the 3D fiber distributions at least six direction arrangements are needed to build the fiber-reinforced isotropic composite materials. The results of the FEM simulations are consistent with those of our expressions %$\widehat{\mathbf {C}}%$. Zhang, Lei verfasserin aut Huang, Mojia verfasserin aut Enthalten in Acta mechanica Wien : Springer, 1965 230(2019), 12 vom: 12. Aug., Seite 4175-4195 (DE-627)270126139 (DE-600)1476343-6 1619-6937 nnns volume:230 year:2019 number:12 day:12 month:08 pages:4175-4195 https://dx.doi.org/10.1007/s00707-019-02485-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 50.31 ASE 50.33 ASE 33.11 ASE AR 230 2019 12 12 08 4175-4195 |
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10.1007/s00707-019-02485-w doi (DE-627)SPR007513062 (SPR)s00707-019-02485-w-e DE-627 ger DE-627 rakwb eng 530 ASE 50.31 bkl 50.33 bkl 33.11 bkl Zhao, Tengfei verfasserin aut Effective elasticity tensors of fiber-reinforced composite materials with 2D or 3D fiber distribution coefficients 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract A fiber-reinforced composite material %$\mathcal {N}%$ consists of a matrix and numerous fibers. Besides their intrinsic properties and the volume fractions of matrix and fibers, the effective elasticity tensors of %$\mathcal {N}%$ are also related to the two-dimensional (2D) or the three-dimensional (3D) fiber direction distributions. Herein the Fourier series and the Wigner D-functions are introduced as the 2D and the 3D fiber direction distribution functions (FDF), respectively. The expanded coefficients of the FDF are called the fiber distribution coefficients (FDC). When %$\mathcal {N}%$ consists of an anisotropic elasticity matrix and numerous transversely isotropic fibers, we derive the effective elasticity tensor %$\widehat{\mathbf {C}}%$ of %$\mathcal {N}%$ by the self-consistent method with the 2D FDC or the 3D FDC. The FDC can be easily obtained via the fiber direction arrangements of %$\mathcal {N}%$ for the fiber arbitrary or orthorhombic distributions of %$\mathcal {N}%$. The procedure of deriving %$\widehat{\mathbf {C}}%$ is simple because the Kelvin notation is used to compute tensor rotations. When both the matrix and the fibers are isotropic, for the 2D fiber distributions at least three direction arrangements of fibers are needed to build the fiber-reinforced transversely isotropic composite materials, and for the 3D fiber distributions at least six direction arrangements are needed to build the fiber-reinforced isotropic composite materials. The results of the FEM simulations are consistent with those of our expressions %$\widehat{\mathbf {C}}%$. Zhang, Lei verfasserin aut Huang, Mojia verfasserin aut Enthalten in Acta mechanica Wien : Springer, 1965 230(2019), 12 vom: 12. Aug., Seite 4175-4195 (DE-627)270126139 (DE-600)1476343-6 1619-6937 nnns volume:230 year:2019 number:12 day:12 month:08 pages:4175-4195 https://dx.doi.org/10.1007/s00707-019-02485-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 50.31 ASE 50.33 ASE 33.11 ASE AR 230 2019 12 12 08 4175-4195 |
| allfieldsSound |
10.1007/s00707-019-02485-w doi (DE-627)SPR007513062 (SPR)s00707-019-02485-w-e DE-627 ger DE-627 rakwb eng 530 ASE 50.31 bkl 50.33 bkl 33.11 bkl Zhao, Tengfei verfasserin aut Effective elasticity tensors of fiber-reinforced composite materials with 2D or 3D fiber distribution coefficients 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract A fiber-reinforced composite material %$\mathcal {N}%$ consists of a matrix and numerous fibers. Besides their intrinsic properties and the volume fractions of matrix and fibers, the effective elasticity tensors of %$\mathcal {N}%$ are also related to the two-dimensional (2D) or the three-dimensional (3D) fiber direction distributions. Herein the Fourier series and the Wigner D-functions are introduced as the 2D and the 3D fiber direction distribution functions (FDF), respectively. The expanded coefficients of the FDF are called the fiber distribution coefficients (FDC). When %$\mathcal {N}%$ consists of an anisotropic elasticity matrix and numerous transversely isotropic fibers, we derive the effective elasticity tensor %$\widehat{\mathbf {C}}%$ of %$\mathcal {N}%$ by the self-consistent method with the 2D FDC or the 3D FDC. The FDC can be easily obtained via the fiber direction arrangements of %$\mathcal {N}%$ for the fiber arbitrary or orthorhombic distributions of %$\mathcal {N}%$. The procedure of deriving %$\widehat{\mathbf {C}}%$ is simple because the Kelvin notation is used to compute tensor rotations. When both the matrix and the fibers are isotropic, for the 2D fiber distributions at least three direction arrangements of fibers are needed to build the fiber-reinforced transversely isotropic composite materials, and for the 3D fiber distributions at least six direction arrangements are needed to build the fiber-reinforced isotropic composite materials. The results of the FEM simulations are consistent with those of our expressions %$\widehat{\mathbf {C}}%$. Zhang, Lei verfasserin aut Huang, Mojia verfasserin aut Enthalten in Acta mechanica Wien : Springer, 1965 230(2019), 12 vom: 12. Aug., Seite 4175-4195 (DE-627)270126139 (DE-600)1476343-6 1619-6937 nnns volume:230 year:2019 number:12 day:12 month:08 pages:4175-4195 https://dx.doi.org/10.1007/s00707-019-02485-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 50.31 ASE 50.33 ASE 33.11 ASE AR 230 2019 12 12 08 4175-4195 |
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Zhao, Tengfei @@aut@@ Zhang, Lei @@aut@@ Huang, Mojia @@aut@@ |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR007513062</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220110194841.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201005s2019 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00707-019-02485-w</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR007513062</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00707-019-02485-w-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">50.31</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">50.33</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">33.11</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Zhao, Tengfei</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Effective elasticity tensors of fiber-reinforced composite materials with 2D or 3D fiber distribution coefficients</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2019</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract A fiber-reinforced composite material %$\mathcal {N}%$ consists of a matrix and numerous fibers. Besides their intrinsic properties and the volume fractions of matrix and fibers, the effective elasticity tensors of %$\mathcal {N}%$ are also related to the two-dimensional (2D) or the three-dimensional (3D) fiber direction distributions. Herein the Fourier series and the Wigner D-functions are introduced as the 2D and the 3D fiber direction distribution functions (FDF), respectively. The expanded coefficients of the FDF are called the fiber distribution coefficients (FDC). When %$\mathcal {N}%$ consists of an anisotropic elasticity matrix and numerous transversely isotropic fibers, we derive the effective elasticity tensor %$\widehat{\mathbf {C}}%$ of %$\mathcal {N}%$ by the self-consistent method with the 2D FDC or the 3D FDC. The FDC can be easily obtained via the fiber direction arrangements of %$\mathcal {N}%$ for the fiber arbitrary or orthorhombic distributions of %$\mathcal {N}%$. The procedure of deriving %$\widehat{\mathbf {C}}%$ is simple because the Kelvin notation is used to compute tensor rotations. When both the matrix and the fibers are isotropic, for the 2D fiber distributions at least three direction arrangements of fibers are needed to build the fiber-reinforced transversely isotropic composite materials, and for the 3D fiber distributions at least six direction arrangements are needed to build the fiber-reinforced isotropic composite materials. The results of the FEM simulations are consistent with those of our expressions %$\widehat{\mathbf {C}}%$.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zhang, Lei</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Huang, Mojia</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Acta mechanica</subfield><subfield code="d">Wien : Springer, 1965</subfield><subfield code="g">230(2019), 12 vom: 12. 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Zhao, Tengfei |
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530 ASE 50.31 bkl 50.33 bkl 33.11 bkl Effective elasticity tensors of fiber-reinforced composite materials with 2D or 3D fiber distribution coefficients |
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Effective elasticity tensors of fiber-reinforced composite materials with 2D or 3D fiber distribution coefficients |
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effective elasticity tensors of fiber-reinforced composite materials with 2d or 3d fiber distribution coefficients |
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Effective elasticity tensors of fiber-reinforced composite materials with 2D or 3D fiber distribution coefficients |
| abstract |
Abstract A fiber-reinforced composite material %$\mathcal {N}%$ consists of a matrix and numerous fibers. Besides their intrinsic properties and the volume fractions of matrix and fibers, the effective elasticity tensors of %$\mathcal {N}%$ are also related to the two-dimensional (2D) or the three-dimensional (3D) fiber direction distributions. Herein the Fourier series and the Wigner D-functions are introduced as the 2D and the 3D fiber direction distribution functions (FDF), respectively. The expanded coefficients of the FDF are called the fiber distribution coefficients (FDC). When %$\mathcal {N}%$ consists of an anisotropic elasticity matrix and numerous transversely isotropic fibers, we derive the effective elasticity tensor %$\widehat{\mathbf {C}}%$ of %$\mathcal {N}%$ by the self-consistent method with the 2D FDC or the 3D FDC. The FDC can be easily obtained via the fiber direction arrangements of %$\mathcal {N}%$ for the fiber arbitrary or orthorhombic distributions of %$\mathcal {N}%$. The procedure of deriving %$\widehat{\mathbf {C}}%$ is simple because the Kelvin notation is used to compute tensor rotations. When both the matrix and the fibers are isotropic, for the 2D fiber distributions at least three direction arrangements of fibers are needed to build the fiber-reinforced transversely isotropic composite materials, and for the 3D fiber distributions at least six direction arrangements are needed to build the fiber-reinforced isotropic composite materials. The results of the FEM simulations are consistent with those of our expressions %$\widehat{\mathbf {C}}%$. |
| abstractGer |
Abstract A fiber-reinforced composite material %$\mathcal {N}%$ consists of a matrix and numerous fibers. Besides their intrinsic properties and the volume fractions of matrix and fibers, the effective elasticity tensors of %$\mathcal {N}%$ are also related to the two-dimensional (2D) or the three-dimensional (3D) fiber direction distributions. Herein the Fourier series and the Wigner D-functions are introduced as the 2D and the 3D fiber direction distribution functions (FDF), respectively. The expanded coefficients of the FDF are called the fiber distribution coefficients (FDC). When %$\mathcal {N}%$ consists of an anisotropic elasticity matrix and numerous transversely isotropic fibers, we derive the effective elasticity tensor %$\widehat{\mathbf {C}}%$ of %$\mathcal {N}%$ by the self-consistent method with the 2D FDC or the 3D FDC. The FDC can be easily obtained via the fiber direction arrangements of %$\mathcal {N}%$ for the fiber arbitrary or orthorhombic distributions of %$\mathcal {N}%$. The procedure of deriving %$\widehat{\mathbf {C}}%$ is simple because the Kelvin notation is used to compute tensor rotations. When both the matrix and the fibers are isotropic, for the 2D fiber distributions at least three direction arrangements of fibers are needed to build the fiber-reinforced transversely isotropic composite materials, and for the 3D fiber distributions at least six direction arrangements are needed to build the fiber-reinforced isotropic composite materials. The results of the FEM simulations are consistent with those of our expressions %$\widehat{\mathbf {C}}%$. |
| abstract_unstemmed |
Abstract A fiber-reinforced composite material %$\mathcal {N}%$ consists of a matrix and numerous fibers. Besides their intrinsic properties and the volume fractions of matrix and fibers, the effective elasticity tensors of %$\mathcal {N}%$ are also related to the two-dimensional (2D) or the three-dimensional (3D) fiber direction distributions. Herein the Fourier series and the Wigner D-functions are introduced as the 2D and the 3D fiber direction distribution functions (FDF), respectively. The expanded coefficients of the FDF are called the fiber distribution coefficients (FDC). When %$\mathcal {N}%$ consists of an anisotropic elasticity matrix and numerous transversely isotropic fibers, we derive the effective elasticity tensor %$\widehat{\mathbf {C}}%$ of %$\mathcal {N}%$ by the self-consistent method with the 2D FDC or the 3D FDC. The FDC can be easily obtained via the fiber direction arrangements of %$\mathcal {N}%$ for the fiber arbitrary or orthorhombic distributions of %$\mathcal {N}%$. The procedure of deriving %$\widehat{\mathbf {C}}%$ is simple because the Kelvin notation is used to compute tensor rotations. When both the matrix and the fibers are isotropic, for the 2D fiber distributions at least three direction arrangements of fibers are needed to build the fiber-reinforced transversely isotropic composite materials, and for the 3D fiber distributions at least six direction arrangements are needed to build the fiber-reinforced isotropic composite materials. The results of the FEM simulations are consistent with those of our expressions %$\widehat{\mathbf {C}}%$. |
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| container_issue |
12 |
| title_short |
Effective elasticity tensors of fiber-reinforced composite materials with 2D or 3D fiber distribution coefficients |
| url |
https://dx.doi.org/10.1007/s00707-019-02485-w |
| remote_bool |
true |
| author2 |
Zhang, Lei Huang, Mojia |
| author2Str |
Zhang, Lei Huang, Mojia |
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270126139 |
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c |
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false |
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| doi_str |
10.1007/s00707-019-02485-w |
| up_date |
2024-07-03T13:26:27.891Z |
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1803564548512284672 |
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| score |
7.399148 |